Represent the following set of points in the XY plane

Question

Represent the following set of points in the XY plane:

{ (x,y) | |x|=1 }

{ (x,y) | |x| is less than or = 1 }

Answer 1

HINT: Note that your set imposes no restriction at all on the $y$-coordinate. If you find a point in the set, every other point with the same $y$-coordinate will also be in the set. Now, what does $\{x\in\Bbb R:|x|\le 1\}$ look like as a subset of the real line?

Added: Your region is the blue stripe in the picture below; it extends infinitely far up and down.

Answer 2

Hint: Can you represent them on the $x$ axis? Note that since the criteria do not depend on $y$ the sets will be vertical lines at all $x$ that are acceptable.